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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">m</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>;<br/>





<a NAME="E1:10"/>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">m</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">m</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">m</font>, <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">m</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T19" title="CAT_1:th.19">CAT_1:19</a>, <a class="ref" href="cat_1.html#T22" title="CAT_1:th.22">CAT_1:22</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">F</font>, <font color="Maroon" title="c5">F1</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c6">t</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F1</font><b> such that </b><br/><a NAME="E3:10"/><i><font color="Green" title="E10">A1</font></i>: 
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F1</font> )
 <b>and </b><br/><a NAME="E4:10"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T40" title="NATTRA_1:th.40">NATTRA_1:40</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">F</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c5">F1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c6">t</font>
;<br/>

<a NAME="E5:10"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D18" title="NATTRA_1:def.18">NATTRA_1:def 18</a></i>;<br/>
<b>hence </b><a NAME="E6:10"/>
<font color="Maroon" title="c4">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F1</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E4:10"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="nattra_1.html#T35" title="NATTRA_1:th.35">NATTRA_1:35</a></i>;<br/>

<b>thus </b><a NAME="E7:10"/>
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F1</font> &amp; <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">F1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="isocat_2.html#E3:10"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="isocat_2.html#E4:10"><i><font color="Green" title="E11">A2</font></i></a></i>;<br/>


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